BNAD 277- Exam 1 (Conceptual Questions)

A new sales training program has been instituted at a rent-to-own company. Prior to the training, 6 employees were tested on their knowledge of products offered by the company. Once the training was completed, the employees were tested again in an effort to determine whether or not the training program was effective. Scores are known to be normally distributed. The sample scores on the tests are listed next. Use pretest score as μ1 for population 1 and posttest score as μ2 for population 2, or μD as the difference calculated as pretest score minus posttest score.

0.57

If there are five treatments under study, the number of pairwise comparisons is _______.

10

Use the incomplete ANOVA table to answer questions 17-21 17. For the within groups category, the df are 18. The sum of the squares due to treatments is 19. The mean square error is 20 The value of the test statistic is 21. At the 5% significance level, the critical value is

17. 8 18. 25 19. 9.375 20. 1.333 21. 4.46

In a two-way ANOVA test, how many null hypotheses are tested?

2

What are the degrees of freedom for the Jarque-Bera goodness-of-fit test for normality?

2

Use the following data for questions 43-47 A card-dealing machine deals spades (1), hearts (2), clubs (3), and diamonds (4) at random as if from an infinite deck. In a randomness check, 1,600 cards were dealt and counted. The results are shown below. Spades - 410 Hearts - 405 Clubs - 370 Diamonds - 415 43. To test if the poker-dealing machine deals cards at random, the null and alternative hypotheses are ________________________________________. 44. Using the problem above, for the goodness-of-fit test, the degrees of freedom are ____. 45. Using the problem above, for the goodness-of-fit test, the value of the test statistic is _____. 46. Using the problem above, at the 5% significance level, the critical value is ______. 47. Using either the critical value approach or p-value approach, the decision and conclusion from above are _________________________________________.

43. Ho: p1 = p2=p3=p4=0.25 Ha: Not all population proportions are equal to 0.25 44. 3 45. 3.125 46. 7.815 47. do not reject the null hypoth., we cannot could that not all of the proportions are equal to 0.25

Use the following data for questions 57-61: In the following table, likely voters' preferences of two candidates are cross-classified by gender. Candidate A: Male - 150 Female - 130 Candidate B: Male - 100 Female - 120 57. To test that gender and candidate preference are independent, the null hypothesis is ___________________________. 58. Using above, for the chi-square test of independence, the assumed degrees of freedom are 59. Using above, for the chi-square test of independence, the value of the test statistic is _______. 60. Using above, At the 10% significance level, the critical value is _______. 61. Using either the critical value approach or p-value approach, the decision and conclusion are _________________________________________.

57. Ho: Gender and candidate preference are independent 58. 1 59. 3.25 60. 2.706 61. reject the null hypoth.; gender and candidate preference are dependent

In the test for comparing two population means when population variances are unknown and unequal, a student calculates the degrees of freedom using the proper formula as 61.75. Per the t-table you were given, how many degrees of freedom should the student use to find the critical value or p-value of the test?

60

A university wants to compare out-of-state applicants' mean SAT math scores (μ1) to in-state applicants' mean SAT math scores (μ2). The university looks at 35 in- state applicants and 35 out-of-state applicants. The mean SAT math score for in- state applicants was 540, with a standard deviation of 20. The mean SAT math score for out-of-state applicants was 555, with a standard deviation of 25. It is reasonable to assume the corresponding population standard deviations are equal. To calculate the confidence interval for the difference μ1 - μ2, what is the number of degrees of freedom of the appropriate probability distribution?

68

The following table shows the distribution of employees in an organization. Martha Foreman, an analyst, w ants to see if race has a bearing on the position a person holds with this company. (Look at table) 68. Assuming that race and seniority are independent, which of the following is the expected frequency of Asian directors? 69. For the chi-square test for independence, the degrees of freedom used are _____.

68. 1.95 69. 9

A particular personal trainer works primarily with track and field athletes. She believes that her clients run faster after going through her program for six weeks. How might she test that claim?

A matched pairs hypothesis test for Ud

Suppose you want to determine if gender and major are dependent. Which of the following tests should you use?

Chi-square test for independence

Using the scenario above, which of the following is the appropriate decision given a 5% level of significance?

Conclude that the mean attendance differs

A farmer uses a lot of fertilizer to grow his crops. The farmer's manager thinks fertilizer products from distributor A contain more of the nitrogen that his plants need than distributor B's fertilizer does. He takes two independent samples of four batches of fertilizer from each distributor and measures the amount of nitrogen in each batch. Fertilizer from distributor A contained an average of 23 pounds per batch and fertilizer from distributor B contained an average of 18 pounds per batch. Suppose the population standard deviation for distributor A and distributor B is four pounds per batch and five pounds per batch, respectively. Assume the distribution of nitrogen in fertilizer is normally distributed. Let μ1and μ2 represent the average amount of nitrogen per batch for fertilizer's A and B, respectively. Which of the following is the appropriate conclusion at the 5% significance level?

Fail to reject Ho; we cannot conclude that the mean amount of fertilizer per batch for distributor A is greater than the amount of fertilizer per batch for distributor B

If the underlying populations cannot be assumed to be normal, then by the central limit theorem, the sampling distribution of 𝑿𝟏 − 𝑿𝟐 is approximately normal only if the sum of the sample observations is sufficiently large—that is, when 𝒏𝟏 + 𝒏𝟐 ≥ 𝟑𝟎

False

Which of the following is the correct alternative hypothesis for the Jarque-Bera test for normality?

Ha: the data is not normally distributed

You would like to determine if there is a higher proportion of smoking among women than among men in a neighborhood. Let women and men be represented by populations 1 and 2, respectively. Which of the following hypotheses is relevant to this claim?

Ho: p1- p2 < 0, Ha; p1- p2 > 0

Which of the following null hypotheses is used to test if five population proportions are the same

Ho: p1=p2=p3=p4=p5= 0.20

Which of the following pairs of hypotheses are used to test if the mean of the first population is smaller than the mean of the second population, using independent random sampling?

Ho: u1 - u2 > (Greater than and equal to) 0, Ha: u1-u2 < 0

A demographer wants to measure life expectancy in countries 1 and 2. Let 𝝁𝟏 and 𝝁𝟐 denote the mean life expectancy in countries 1 and 2, respectively. Specify the hypothesis to determine if life expectancy in country 1 is more than 10 years higher than in country 2.

Ho: u1-u2 <10, Ha: u1-u2 >10

Which of the following is the correct interpretation of the Fisher's 100(1 - α)% confidence interval for μi - μj?

If the interval does not include zero, the null hypothesis is rejected at a level of significance

Suppose you want to perform a test to compare the mean GPA of all freshmen with the mean GPA of all sophomores in a college? What type of sampling is required for this test?

Independent sampling with quantitative data

The heights (in cm) for a random sample of 60 male employees of S&M Construction Company were measured. The sample mean is 166.5, the standard deviation is 12.57, the sample kurtosis is 0.12, and the sample skewness is −0.23. Suppose the null hypothesis of normality is rejected. Which of the following is a valid conclusion?

The heights do not follow a normal distribution

When testing the difference between two population means under independent sampling, we use the z distribution if _________ .

The population variances are known

When calculating the standard error of 𝑿𝟏 − 𝑿𝟐 , under what assumption do you pool the sample variances 𝒔𝟐 and 𝒔𝟐

Unknown population variance that are assumed equal

The heights (in cm) for a random sample of 60 male employees of S&M Construction Company were measured. The sample mean is 166.5, the standard deviation is 12.57, the sample kurtosis is 0.12, and the sample skewness is −0.23. The value of the Jarque-Bera test statistic is ______.

We cannot conclude that the data are not normally distributed

A 7,000-seat theater is interested in determining whether there is a difference in attendance between shows on Tuesday evening and those on Wednesday evening. Two independent samples of 25 weeks are collected for Tuesday and Wednesday. The mean attendance on Tuesday evening is calculated as 5,500, while the mean attendance on Wednesday evening is calculated as 5,850. The known population standard deviation for attendance on Tuesday evening is 550 and the known population standard deviation for attendance on Wednesday evening is 445. Which of the following is the absolute value of the appropriate test statistic?

Zstat= 2.4736

When comparing two population means, their hypothesized difference

may assume any value

For the goodness-of-fit test, the sum of the expected frequencies must equal __

n

Tukey's (HSD) method ensures that the probability of a Type I error remains fixed irrespective of the number of ______________

pairwise comparisons

When using Fisher's LSD method at some stated significance level, the probability of committing a Type I error increases as the number of

pairwise comparisons increases

If units within each block are randomly assigned to each of the treatments, then the design of the experiment is referred to as a ______________________

randomized block design

If the amount of variability between treatments is significantly greater than the amount of variability within treatments, then _________.

reject the null hypothesis of equal population means

For the chi-square test of independence, the expected cell frequencies are found as ________________.

the row total multiplied by the column total divided by the sample size

The calculation of the Jarque-Bera test statistic involves___________.

the sample size, skewness, and kurtosis

Which of the following is the absolute value of the appropriate test statistic if SD=3.764?

tstat= 2.492

The chi-square test of independence is a test of independence for

two qualitative variables

A goodness-of-fit test analyzes two qualitative variables whereas a chi-square test of a contingency table is for a single qualitative variable.

False

ANOVA is a statistical technique used to determine if differences exist between the means of two populations.

False

For a multinomial experiment with k categories, the goodness-of-fit test statistic is assumed to follow a chi-square distribution with k degrees of freedom.

False

The same formulas are used to compute the test statistic whether the hypothesized difference between population proportions is zero or not.

False

Two random samples are considered independent if the observations in the first sample are different from the observations of the second sample.

False

1. When using Fisher's least difference (LSD) method at some stated significance level α, the probability of committing a Type I error increases as the number of pairwise comparisons increases.

True

For a chi-square goodness-of-fit test, the expected category frequencies are calculated using the sample category proportions.

True

For the Jarque-Bera test for normality, the test statistic is assumed to have a chi- square distribution with two degrees of freedom.

True

In the case when 𝝈𝟐 and 𝝈𝟐 are unknown and can be assumed equal, we can calculate a pooled estimate of the variance.

True

The chi-square test statistic measures the difference between the observed frequencies and the expected frequencies assuming the null hypothesis is true.

True

The difference between the two sample means 𝑿𝟏 − 𝑿𝟐 is an interval estimator of ̅̅ the difference between two population means 𝝁𝟏 − 𝝁𝟐 .

True

We use ANOVA to test for differences between population means by examining the amount of variability between the samples relative to the amount of variability within the samples.

True

What type of test for population means should be performed when examining a situation in which employees are first tested, then trained, and finally retested?

a t test under depended or matched pair sampling

The chi-square test of independence is valid when the expected cell frequencies are _______________.

at least 5

For the goodness-of-fit test, the chi-square test statistic will _________________

be greater than or equal to zero

Packaged candies have three different types of colors. Suppose you want to determine if the population proportion of each color is the same. The most appropriate test is the ______

goodness- of- fit test for a multinomial experiment